Authors: | Žunić, Joviša |

Title: | The discrete moments of the circles |

Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume: | 1568 |

First page: | 41 |

Last page: | 49 |

Conference: | 8th International Conference on Discrete Geometry for Computer Imagery, DGCI 1999; Marne-la-Vallee; France; 17 March 1999 through 19 March 1999 |

Issue Date: | 1-Jan-1999 |

Rank: | M21 |

ISBN: | 978-3-540-65685-5 |

ISSN: | 0302-9743 |

DOI: | 10.1007/3-540-49126-0_4 |

Abstract: | The moment of (p,q)-order, mp,q(C), of a circle C given by (x-a)2 + (y-b)2 ≤ r2, is defined to be (Formula Presented). It is naturally to c assume that the discrete moments dmp,q(C), defined as (Formula Presented) can be a good approximation for mp,q(C). This paper gives an answer what is the order of magnitude for the difference between a real moment mp,q(C) and its approximation dmp,q(C), calculated from the corresponding digital picture. Namely, we estimate (Formula Presented) in function of the size of the considered circle C and its center position if p and q are assumed to be integers. These differences are upper bounded with (Formula Presented), where e is an arbitrary small positive number. The established upper bound can be understood as very sharp. The result has a practical importance, especially in the area of image processing and pattern recognition, because it shows what the picture resolution should be used in order to obtain a required precision in the parameter estimation from the digital data taken from the corresponded binary picture. |

Keywords: | Digital geometry | Discrete shapes | Parameter estimation |

Publisher: | Springer Link |

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